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3 years ago

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At an electronics store, a smart phone is on sale for 35% off the original price of $679. If you use the store credit card, you

can receive an additional 15% off the sale price. What is the final price of the smart phone if you use the store credit car

1 answer:

kifflom [539]3 years ago

8 0

Answer:

The final price of the smart phone if you use the store credit card is $339.5

Step-by-step explanation:

Given;

original price of the smart phone = $679

initial discount = 35%

additional discount if you use the store credit card = 15%

total discount of the smart phone if you use the store credit card

= 35% + 15% = 50%

The final price of the smart phone, if you use the store credit card is given as;

P = 0.5 X $679

P = $339.5

Therefore, the final price of the smart phone if you use the store credit card is $339.5

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Find YZ pls fast correct

noname [10]

Answer:

44

Step-by-step explanation:

<u>According to intersecting chords theorem:</u>

21(2x - 6) = 30(x + 1)
42x - 126 = 30x + 30
42x - 30x = 126 + 30
12x = 156
x = 156/12
x = 13

<u>Find the value of YZ:</u>

YZ = 30 + 13 + 1 = 44

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2 years ago

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REY [17]

Answer:

84

Step-by-step explanation:

they are all equal sides so what you'd do is 28+28+28= 84

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3 years ago

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There were 26 students in the classroom. 14 of the students went to the cafeteria and the rest went to the gym. What percentage

OverLord2011 [107]

Answer:

About 53% percent of the students went to the cafeteria.

Step-by-step explanation:

there are 26 students and 14 left that can be put into the fraction 14/26.

To find the percentage you then divide 14 by 26 and turn it into a percent and you get something like 53.846... but you can simplify it to 53%

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2 years ago

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Three of these fractions are equivalent: B. 12 C . 21 D. 74 30 A. . 70 Which one is the odd one out?

IrinaVladis [17]

Answer:

12/30

Step-by-step explanation:

Here is the complete question

Three of these fractions are equivalent A.30/70 B.12/30 C.9/21 D.6/14 which one is the odd one out

to determine the equivalent fractions, convert the fractions to percentage

$\frac{30}{70}$ × 100 = 42.86%

$\frac{12}{30}$ × 100 = 40%

$\frac{9}{21}$ × 100 = 42.86%

$\frac{6}{14}$ x 100 = 42.86%

Another method is to convert the fraction to its simplest form

30/70

To transform to the simplest form. divide both the numerator and the denominator by 10 = 3/7

12/30

To transform to the simplest form. divide both the numerator and the denominator by 6 = 2/5

9/21

To transform to the simplest form. divide both the numerator and the denominator by 3 = 3/7

6/14

To transform to the simplest form. divide both the numerator and the denominator by 2 = 3/7

Using either methods, 12/30 is the odd one out

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3 years ago

Name/ Uid:1. In this problem, try to write the equations of the given surface in the specified coordinates.(a) Write an equation

Gemiola [76]

To find:

(a) Equation for the sphere of radius 5 centered at the origin in cylindrical coordinates

(b) Equation for a cylinder of radius 1 centered at the origin and running parallel to the z-axis in spherical coordinates

Solution:

(a) The equation of a sphere with center at (a, b, c) & having a radius 'p' is given in cartesian coordinates as:

$(x-a)^{2}+(y-b)^{2}+(z-c)^{2}=p^{2}$

Here, it is given that the center of the sphere is at origin, i.e., at (0,0,0) & radius of the sphere is 5. That is, here we have,

$a=b=c=0,p=5$

That is, the equation of the sphere in cartesian coordinates is,

$(x-0)^{2}+(y-0)^{2}+(z-0)^{2}=5^{2}$

$\Rightarrow x^{2}+y^{2}+z^{2}=25$

Now, the cylindrical coordinate system is represented by $(r, \theta,z)$

The relation between cartesian and cylindrical coordinates is given by,

$x=rcos\theta,y=rsin\theta,z=z$

$r^{2}=x^{2}+y^{2},tan\theta=\frac{y}{x},z=z$

Thus, the obtained equation of the sphere in cartesian coordinates can be rewritten in cylindrical coordinates as,

$r^{2}+z^{2}=25$

This is the required equation of the given sphere in cylindrical coordinates.

(b) A cylinder is defined by the circle that gives the top and bottom faces or alternatively, the cross section, & it's axis. A cylinder running parallel to the z-axis has an axis that is parallel to the z-axis. The equation of such a cylinder is given by the equation of the circle of cross-section with the assumption that a point in 3 dimension lying on the cylinder has 'x' & 'y' values satisfying the equation of the circle & that 'z' can be any value.

That is, in cartesian coordinates, the equation of a cylinder running parallel to the z-axis having radius 'p' with center at (a, b) is given by,

$(x-a)^{2}+(y-b)^{2}=p^{2}$

Here, it is given that the center is at origin & radius is 1. That is, here, we have, $a=b=0,p=1$ . Then the equation of the cylinder in cartesian coordinates is,

$x^{2}+y^{2}=1$

Now, the spherical coordinate system is represented by $(\rho,\theta,\phi)$

The relation between cartesian and spherical coordinates is given by,

$x=\rho sin\phi cos\theta,y=\rho sin\phi sin\theta, z= \rho cos\phi$

Thus, the equation of the cylinder can be rewritten in spherical coordinates as,

$(\rho sin\phi cos\theta)^{2}+(\rho sin\phi sin\theta)^{2}=1$

$\Rightarrow \rho^{2} sin^{2}\phi cos^{2}\theta+\rho^{2} sin^{2}\phi sin^{2}\theta=1$

$\Rightarrow \rho^{2} sin^{2}\phi (cos^{2}\theta+sin^{2}\theta)=1$

$\Rightarrow \rho^{2} sin^{2}\phi=1$ (As $sin^{2}\theta+cos^{2}\theta=1$ )

Note that $\rho$ represents the distance of a point from the origin, which is always positive. $\phi$ represents the angle made by the line segment joining the point with z-axis. The range of $\phi$ is given as $0\leq \phi\leq \pi$ . We know that in this range the sine function is positive. Thus, we can say that $sin\phi$ is always positive.

Thus, we can square root both sides and only consider the positive root as,

$\Rightarrow \rho sin\phi=1$

This is the required equation of the cylinder in spherical coordinates.

Final answer:

(a) The equation of the given sphere in cylindrical coordinates is $r^{2}+z^{2}=25$

(b) The equation of the given cylinder in spherical coordinates is $\rho sin\phi=1$

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3 years ago